IC-NRLF 


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GIFT   OF 


A  THEORY  OF  GRAVITATION 
AND  RELATED  PHENOMENA 


BY 

W.   J.  SPILLMAN 


PRESS  OF 

THE  NEW  ERA  PRINTING  COMPANY 
LANCASTER,  PA. 

1915 


A  THEORY  OF  GRAVITATION 
AND  RELATED  PHENOMENA 


BY 

W.   J.  SPILLMAN 


PRESS  OF 

THE  NEW  ERA  PRINTING  COMPANY 
LANCASTER,  PA. 

I9IS 


A  THEORY  OF  GRAVITATION  AND  RELATED 
PHENOMENA. 

BY  W.   J.   SPILLMAN. 

Newton  pointed  out  that  if  there  there  were  a  pressure  in 
the  ether  about  a  body,  and  if  this  pressure  diminishes  as  we 
approach  the  body,  and  if  this  diminution  varies  inversely  as 
the  distance  from  the  body,  gravitation  would  be  accounted  for. 
If,  now,  we  can  find  some  mechanism  that  will  maintain  a 
pressure  in  the  ether  like  that  just  described,  we  can  account 
for  gravitation. 

It  can  be  shown  that  there  is  such  a  mechanism,  if  the  follow- 
ing assumptions  are  granted. 

FUNDAMENTAL  ASSUMPTIONS. 

The  ether. — The  ether  is  assumed  to  exist  in  the  interstices  of 
matter  and  in  open  space.  It  is  assumed  to  be  capable  of  dis- 
tortion by  finite  force,  and  to  oppose  such  distorting  force  with 
an  equal  opposite  force.  In  other  words,  every  point  of  the 
ether  has  a  position  which  it  normally  occupies,  and  when 
removed  from  that  position  tends  forcibly  to  return  to  it,  the 
force  being  proportional  to  the  distortion.  It  is  further  assumed 
that  distortion  at  a  given  point  in  the  ether  tends  to  become 
distributed  in  the  surrounding  ether  according  to  the  law  of 
inverse  squares,  and  that  such  distribution  occurs  at  a  finite 
rate  (the  velocity  of  light). 

The  electron. — It  is  assumed  that  in  the  immediate  vicinity  of 
the  electron  there  is  a  region  of  maximum  permanent  ether  dis- 
tortion, the  distortion  at  other  points  in  the  surrounding  ether 
varying  inversely  as  the  square  of  the  distance  from  the  center 
of  the  electron,  and  that  pressures  are  transmitted  at  a  higher 
velocity  through  distorted  than  through  non-distorted  ether. 

The  permanent  distortion  of  the  ether  in  the  vicinity  of  the 
electron  may  be  conceived  of  as  a  pushing  back  of  the  ether 
radially  from  the  center  of  the  electron,  as  if  an  impenetrable  and 


2  THEORY  OF   GRAVITATION  AND   RELATED   PHENOMENA. 

inelastic  body  were  injected  into  the  midst  of  an  elastic  body; 
or  it  may  be  conceived  of  as  being  circular,  in  two  hemispheres 
facing  each  other,  and  opposite  in  direction  in  the  two  hemi- 
spheres. 

In  explaining  the  phenomena  of  inertia,  electric  currents, 
magnetism,  chemical  affinity,  and  radiant  energy,  the  above 
alternative  assumptions  concerning  the  character  of  the  dis- 
tortion lead  to  essentially  similar  lines  of  reasoning,  but  the 
treatment  on  the  assumption  of  radial  distortion  is  very  much 
simpler.  For  this  reason  it  is  used  here.  In  the  case  of  static 
electricity  only  the  assumption  of  circular  distortion,  opposite 
in  direction  in  the  two  kinds  of  electric  elements,  will  explain 
the  facts.  The  extension  of  the  theory  to  static  electricity  is 
left  for  future  treatment.  It  must  be  remembered,  however, 
that  the  development  of  the  theory  on  the  basis  of  radial  dis- 
tortion differs  only  in  detail,  not  in  principle,  fiom  that  on  the 
basis  of  circular  distortion. 

The  Atom. — The  atom  is  assumed  to  consist,  at  least  in  part, 
of  a  Saturnian  system  of  electrons  in  rapid  orbital  motion.  It 
will  be  shown  that  such  orbital  motion,  with  the  assumptions 
here  made,  would  give  rise  to  a  pressure  in  the  ether  such  as 
Newton  showed  would  account  for  gravitation. 

Physicists  are  agreed  that  the  phenomena  of  inertia,  the 
electric  current,  magnetism,  and  possibly  also  chemical  affinity 
are  probably  related  to  each  other  in  such  manner  that  when  we 
find  the  explanation  of  one  of  them  this  explanation  will  also 
throw  light  on  the  others.  It  will  be  seen  in  what  follows  that 
the  theory  of  gravitation  here  presented  appears  also  to  offer 
suggestions  as  to  the  nature  of  these  other  forces,  as  well  as 
a  possible  explanation  of  them. 

INERTIA. 

Let  c,  Fig.  la,  be  an  electron  stationary  in  the  ether.  At  a 
certain  undetermined  distance  from  the  center  of  this  electron 
(equal  to  what  we  may  call  its  radius)  we  may  assume  a  maxi- 
mum radial  distortion  of  the  ether,  and  we  may  regard  the 
spherical  shell  at  this  distance  as  the  surface  of  the  electron. 
The  distortion  at  this  surface  is  a  maximum  with  reference  to 


THEORY  OF  GRAVITATION  AND   RELATED   PHENOMENA. 


the  distortion  at  greater  distances,  but  not  necessarily  so  for 
that  at  smaller  distances.  With  the  electron  at  rest,  all  distor- 
tion due  to  its  presence  is  radial,  and  hence  the  resisting  forces 
are  all  directed  toward  the  center  of  the  electron.  If  we  imagine 
lines  of  position  which  would  be  straight  lines  radiating  from 
the  position  of  the  center  of  the  electron  if  the  electron  were 
absent,  the  only  modification  of  these  lines  caused  by  the  presence 
of  the  motionless  electron  would  be  to  shorten  them. 


a 


b 

FIG.  i. 


Suppose,  now,  that  for  a  brief  interval  a  force  be  applied  to  the 
electron  tending  to  move  it  in  the  direction  of  the  arrow  in  Fig. 
ib.  The  ether  in  front  of  the  electron  now  tends  to  be  forced 
around  behind  it,  and  the  lines  of  position  perpendicular  to  the 
direction  of  the  force  are  bent  to  the  left  (Fig.  ib).  The  bend 
in  these  lines  would  proceed  outward  wave-fashion,  at  the  velocity 
of  light.  The  bent  condition  of  these  lines  corresponds  to  lateral 
distortion  of  the  ether,  which  gives  rise  to  forces  tending  to 
crowd  the  ether  back  in  front  of  the  electron,  thus  opposing  the 
force  tending  to  move  the  electron.  This  opposing  force  is 
identified  as  that  due  to  the  inertia  of  matter. 

If,  now,  the  moving  force  cease,  the  conditions  in  the  ether 
about  the  electron  an  instant  later  are  as  shown  in  Fig.  ic. 
(Since  the  electron  is  now  in  motion,  the  lines  of  position  change 
their  position  in  the  ether,  for  they  are  imaginary  lines  radiating 
from  the  center  of  the  electron.)  There  being  no  longer  any 
distorting  force  acting  through  the  electron  on  the  ether,  the 
lines  of  position  resume  their  normal  form,  first  at  the  surface  of 
the  electron,  and  progressively  later  at  greater  distances,  leaving 
a  spherical  shell  of  distortion  moving  outward  as  an  ether  wave 
with  the  velocity  of  light. 


4  THEORY   OF   GRAVITATION   AND   RELATED   PHENOMENA. 

If,  now,  any  force  oppose  the  motion  of  the  electron,  the  condi- 
tions shown  in  the  vertical  lines  of  position  in  Fig.  ib  are  reversed, 
the  ether  becoming  distorted  in  such  manner  as  to  press  the 
electron  forward.  Thus  inertia  opposes  any  change  in  the 
condition  of  rest  or  motion  of  a  body. 

UNIFORM  MOTION  IN  A  STRAIGHT  LINE. 
When  an  electron  moves  with  uniform  velocity  in  a  straight 
line,  the  only  distortion  of  the  ether  about  it  is  radial,  and  the 
lines  of  position  radiating  from  it  are  straight.  But  since  the 
amount  of  distortion  varies  inversely  as  the  square  of  the  distance 
from  the  electron,  and  since  the  distances  between  the  electron 
and  the  points  of  the  ether  about  it  are  changing,  it  follows  that 
the  condition  of  distortion  is  changing  at  every  point  in  the 
surrounding  ether.  This  means  that  every  point  of  ether  is 
moving,  the  motion  being  such  as  to  maintain  a  constant  condi- 
tion of  radial  distortion  about  the  moving  electron.  What  is 
the  character  of  the  motion  of  a  particular  point  of  ether  at  any 
particular  instant?  A  moment's  consideration  will  show  that 
the  movement  directly  in  front  of  the  electron  must  be  in  the 
same  direction  as  that  in  which  the  electron  is  moving.  Directly 
abreast  of  the  electron  the  motion  of  the  ether  must  be  in  exactly 
the  opposite  direction.  Also,  the  amount  of  motion  of  any 
point  varies  inversely  as  the  square  of  the  distance  to  the  center 
of  the  electron.  The  direction  of  movement  at  other  points 
may  be  found  as  follows: 


X 


FIG.  2. 


Let  C  (Fig.  2)  be  an  electron  moving  in  the  direction  CX  with 
velocity  (V=)CH.  Let  CE  be  any  line  passing  through  C. 
Then  GH,  parallel  to  CE,  will  represent  C's  velocity  in  the 
direction  CE,  and  CG  will  be  C's  velocity  in  the  direction  CG, 


THEORY  OF   GRAVITATION  AND   RELATED   PHENOMENA.'          5 

perpendicular  to  CE.  Let  P  be  any  point  on  the  line  CE.  Let 
the  ratio  of  the  velocity  (v)  of  P  to  the  velocity  of  C  be  i/R2. 
Then  v  =  V/R2.  Since  the  velocity  of  P  varies  inversely  as  the 
square  of  CP,  the  ratio  i/R2  must  do  the  same.  Let  Pb  =  the 
component  of  P's  motion  perpendicular  to  CE,  and  ba  =  the 
component  parallel  to  CE.  Then  Pa  =  the  velocity  of  P,  and 
shows  the  direction  of  motion  of  P.  Furthermore,  the  angle 
aPE  =  PCX  =  6.  Hence  the  angle  aPd  =  20.  But  26  is  the 
angle  which  the  tangent  to  a  circle  makes  with  the  axis  of  X 
when  this  circle  has  its  center  on  the  axis  of  Y,  and  its  circum- 
ference passes  through  the  origin,  as  seen  in  Fig.  3.  Here  the 


angle  P'PC  =  P'CP  =  6,  and  PP'X  =  P'CP  +  P'PC  =  26. 
Hence  the  direction  of  motion  at  every  point  in  the  ether  about 
C  is  tangent  to  circles  whose  centers  lie  in  the  plane  CY  (Fig.  3), 
and  whose  circumferences  pass  through  C  and  through  the  points 
in  question.  Thus,  the  direction  of  motion  at  any  instant  in 
the  ether  about  a  moving  electron  is  in  exact  circles.  These 
circles  are  all  tangent  to  each  other  at  C,  their  centers  lie  in  the 
plane  CY*  they  are  of  all  diameters  from  O  to  oo,  and  they  lie 
in  every  possible  plane  passing  through  CX  (Fig.  3). 

Electrical  Attraction. 

Let  a  and  b,  Fig.  4,  represent  two  electrons  moving  parallel 
to  each  other.  In  the  arcs  aPb  the  motion  which  a  tends  to 
set  up  is  opposed  by  the  motion  which  b  tends  to  set  up.  Hence 
there  will  be  pressure  generated  in  these  arcs,  and  in  a  direction 
tangential  to  them.  But  such  pressure  tends  to  move  the  ether 
toward  the  right.f  There  is  thus  pressure  generated  to  the 

*  That  is,  in  the  plane  produced  by  the  revolution  of  CY  about  CX. 
t  See  paragraph  one  under  Gravitation,  beyond. 


6  THEORY  OF  GRAVITATION  AND   RELATED    PHENOMENA. 

right  of  these  arcs,  while  a  partial  pressure  vacuum  forms  behind 
them.  The  ether  pressure  between  the  electrons  is  thus  reduced, 
and  the  electrons  are  driven  toward  each  other  by  the  greater 


FIG.  4. 

pressure  on  their  distal  surfaces.  This  represents  the  conditions 
existing  in  two  parallel  currents  of  electricity,  and  is  offered  as 
an  explanation  of  the  attraction  between  them. 

Electrical  Repulsion. 

In  Fig.  5,  let  a  and  b  represent  two  electrons  moving  in  oppo- 
site directions.     Let  P  represent  a  point  in  the  ether  midway 


FIG.  5. 

between  them,  and  Pr  a  point  on  the  opposite  side  of  one  of 
them  from  the  other.  Electron  a  tends  to  move  the  ether  to 
the  right  at  both  P  and  Pf .  Electron  b  tends  to  move  it  in 
the  opposite  direction.  Hence  pressure  is  generated  at  both 
points.  But  the  pressure  at  P'  is  smaller  than  that  at  P  in 
the  inverse  ratio  of  the  square  of  the  distance  from  b.  Not 
only  that,  but  the  pressure  at  P'  is  away  from  both  electrons. 
We  thus  have  increased  pressure  in  the  ether  between  the  elec- 
trons, and  decreased  pressure  in  the  ether  on  their  outer  sides. 
Hence  they  are  driven  apart.  This  seems  to  be  the  explanation 
of  electrical  repulsion  in  parallel  circuits  in  which  the  currents 
are  flowing  in  opposite  directions. 


THEORY  OF  GRAVITATION  AND   RELATED   PHENOMENA.  7 

Induced  Currents. 

Let  L  and  L',  Fig.  6,  represent  parallel  portions  of  two  closed 
circuits.  B  is  a  battery  arranged  to  send  current  through  L. 
Let  the  arrow  show  the  direction  in  which  the  electrons  move 
in  this  current.  When  the  circuit  L  is  first  closed,  a  stream  of 


L' 


FIG.  6. 

electrons  passes  into  L.  This  sets  up  motion  of  the  ether  in  L' 
toward  the  left.  This  movement  of  the  ether  creates  stresses 
against  the  electrons  in  Z/,  tending  to  drive  them  toward  the  left, 
thus  giving  rise  to  a  counter  induced  current.  Any  increase  of 
current  in  L  will  similarly  cause  an  inverse  current  in  V '. 

After  the  current  becomes  constant  in  L,  the  following  condi- 
tions obtain:  because  of  resistance  in  the  conductor,  force  must 
be  exerted  on  the  electrons  to  keep  them  moving.  This  force 
originates  in  the  generator  (battery  or  dynamo),  and  is  propa- 
gated along  the  conductor  much  as  pressure  is  in  a  gas,  utilizing 
the  mutual  repulsion  of  the  electrons.  Because  of  this  urging 
force  (electromotive  force),  the  inertia  of  the  particles  is  brought 
into  play  and  a  state  of  stress  in  the  ether  about  the  conductor  is 
produced  similar  to  that  shown  in  Fig.  ib.  In  other  words,  the 
ether  about  the  conductor  is  displaced  in  a  direction  opposite  to 
that  in  which  the  electrons  move.  The  energy  which  will  oppose 
stoppage  of  the  current  is  thus  stored  up  in  the  stressed  ether 
about  the  conductor. 

If,  now,  the  current  in  L  diminish,  the  stress  in  the  ether  is 
reduced,  and  an  impulse  moves  off  into  space  causing  a  slight 
movement  of  the  ether  in  the  direction  of  the  cut  rent;  that  is, 
the  bent  ether  partly  unbends.  Free  electrons  in  L'  are  thus 
given  an  impulse  in  the  direction  of  the  current  in  L,  giving  lise 
to  a  direct  current  in  L' '. 


8  THEORY   OF  GRAVITATION  AND  RELATED   PHENOMENA. 

The  phenomena  of  electric  currents  indicate  that  there  are 
electrons  in  and  about  the  atoms  of  conductors  that  are  not 
integral  parts  of  these  atoms.  These  semi-free  electrons  are 
probably  held  in  the  vicinity  of  the  atoms  by  attractions  exerted 
by  the  atoms.  Possibly  they  are  vibrating  back  and  forth 
through  the  atoms,  or  revolving  about  them.  A  surge  in  the 
ether  would  carry  certain  of  these  electrons  out  of  the  sphere  of 
action  of  one  atom  into  that  of  another.  But  these  electrons 
would  enter  the  sphere  of  the  new  atom  with  sufficient  velocity 
to  carry  them  beyond  to  another  atom.  An  electric  current 
may  thus  be  pictured  as  a  series  of  electrons  swinging  from 
one  atom  to  another  in  a  conductor.  This,  of  course,  is  only  a 
suggestion  as  to  the  nature  of  the  electric  current,  which  may  or 
may  not  represent  the  facts  correctly. 

Magnetism. 

An  electron  moving  in  a  closed  orbit,  as  is  supposed  to  be  the 
case  in  atoms,  would,  under  our  assumptions,  cause  every  point 
of  ether  about  it  to  move  in  a  similar  but  smaller  orbit,  the  form 
of  the  orbit  of  any  point  depending  on  the  orientation  of  the 


FIG.  7. 

point  with  reference  to  the  orbit  of  the  electron.  In  Fig.  7  the 
movement  of  electron  c  counterclockwise  in  its  circular  orbit 
causes  the  point  of  ether  p,  lying  on  the  axis  of  c's  orbit,  to 
move  clockwise  in  a  similar  smaller  orbit.  In  all  cases,  the 
movement  of  the  ether  about  an  atom  would  be  perpendicular 
to  the  familiar  lines  of  force  in  the  magnetic  field  of  the  atom. 

Similarly,  the  passage  of  an  electron  through  a  long,  straight 
portion  of  a  conductor  would  cause  the  points  of  ether  about  the 
conductor  to  describe  approximately  circular  but  extremely  small 
orbits,  the  plane  of  each  orbit  passing  through  the  conductor. 
Here  again  the  ether  movement  is  perpendicular  to  the  lines  of 
force  in  the  magnetic  field  about  the  conductor. 


THEORY  OF   GRAVITATION  AND   RELATED   PHENOMENA.  9 

Superposed  magnetic  fields  would  give  rise  to  changes  in  the 
static  pressure  in  the  ether,  raising  it  where  the  fields  are  opposed, 
and  lowering  it  where  they  coincide  in  respect  to  the  ether  move- 
ments in  each.  Magnetic  attraction  and  repulsion  may  thus 
be  accounted  for. 

That  the  strength  of  the  magnetic  field  about  an  atom  varies 
inversely  as  the  cube  of  the  distance  from  the  atom  is  proven 
as  follows:  Let  D  represent  the  distance  of  the  point  c  (Fig.  8) 
from  the  proximal  side  of  the  atom  (i.  e.,  from  electron  a)  and  d 
the  diameter  of  the  atom.  Let  m  represent  the  motion  which  a 
tends  to  produce  at  c,  and  n  the  motion  which  b  tends  to  produce 
at  the  same  point.  Then 

K  K 

m  =--  -pi  ,  and  n  =  /^    .   ^2  ,  K  being  a  constant. 

K  K  2KDd  +  Kd2 

=  D*  ~  (D  +  d?  =     D*(D  +  dY     ~~  the   stren^th  of 

the  field  at  c.     But  d  vanishes  with  reference  to  D  at  ordinary 
distances.     Hence 

2KDd       2Kd 


Hence  the  strength  of  the  magnetic  field  about  an  atom  varies 
inversely  as  the  cube  of  the  distance.  This  is  consistent  with 
experimental  results,  for  the  combined  effect  of  the  two  poles  of 
a  short  magnet  on  another  single  magnetic  pole  is  known  to  vary 
inversely  as  the  cube  of  the  distance.  This  law  does  not  hold 
for  small  distances,  such  as  we  may  suppose  are  concerned  in 
chemical  affinity.  At  the  point  where  D  =  d,  m  -  n  becomes 
equal  to  ^Kj^D\  Hence,  at  that  point  the  magnetic  field 
varies  inversely  as  the  square  of  D. 

GRAVITATION. 

In  developing  a  theory  of  gravitation  from  the  assumptions 
with  which  we  began,  it  is  necessary  for  the  reader  to  recall  a 
familiar  fact  that  must  be  used.  Suppose  a  ring  imbedded,  say, 
in  a  matrix  of  cement.  Now,  if  the  circumference  of  the  ring 


10         THEORY  OF   GRAVITATION  AND   RELATED   PHENOMENA. 

be  increased,  as  it  would  be  by  raising  its  temperature,  the 
ring  will  press  outward  against  the  matrix.  This  outward 
pressure  arises  from  a  tangential  pressure  in  the  circumference 
of  the  ring.  In  general,  a  tangential  pressure  in  an  arc  will 
give  rise  to  outward  pressure  in  the  direction  of  the  convexity 
of  the  arc. 

In  Fig.  8,  A   represents  an  atom,  consisting  of  a  Saturnian 
system  of  electrons,  revolving  as  shown  by  the  arrows. 


-So 


FIG.  8. 

Electron  a  tends  to  move  the  ether  downward  at  c,  d,  e,  /, 
and  g\  i.  e.,  at  all  points  along  the  line  ag,  and  the  velocity  at 
any  point  tends  to  vary  inversely  as  the  square  of  the  distance 
from  a.  Electron  b  tends  to  move  the  ether  upward  at  all  these 
points.  Hence  pressure  is  generated  at  each  of  these  points. 
Since  the  movement  of  the  ether  is  in  the  arcs  of  circles,  concave 
toward  the  atom,  these  pressures  are  propagated  outward,  or 
away  from  the  atom.  Thus  the  pressure  generated  at  c  extends 
outward  from  c  indefinitely.  At  d  the  pressure  generated  at  d 
is  added  to  that  generated  at  c,  so  that  beyond  d  the  pressure 
is  the  sum  of  these  two  pressures.  More  generally,  the  total 
pressure  at  any  point  is  the  sum  of  all  the  pressures  gener- 
ated between  that  point  and  the  atom.  Hence  the  static 
pressure  in  the  ether  is  greater  the  farther  we  get  from  the 
atom.  Let  g  represent  an  electron  floating  in  the  ether.  Now 
the  static  pressure  in  the  ether  on  the  distal  side  of  g  is 
greater  than  on  the  proximal  side.  Hence  g  is  driven  toward  the 
atom.  This  is  taken  to  be  gravitational  attraction.  To  show 
that  this  force  varies  inversely  as  the  square  of  the  distance 
from  the  attracting  booly,  we  have  the  following  considerations. 
The  amount  of  pressure  generated  at  any  point  along  the  line  ag 
varies  inversely  as  the  square  of  the  distance  of  that  point  from 
the  electron  6,  since  b  is  more  distant  than  a,  and  the  amount 


THEORY  OF   GRAVITATION  AND   RELATED   PHENOMENA.         II 

of  pressure  generated  is  limited  by  the  smaller  motion  which  b 
tends  to  give  the  ether.  Therefore  P  =  K/D2,  where  P  is  the 
pressure  generated  at  the  point  under  consideration,  K  a  con- 
stant, and  D  the  distance  of  the  point  from  electron  b.  We  may 
represent  this  equation  graphically,  as  in  Fig.  9,  where  the 


abed 

FIG.  9. 

ordinates  aaf,  bb',  etc.,  represent  the  respective  pressures  gen- 
erated at  the  points  a,  b,  etc.  It  is  plain  that  the  total  pressure 
existing,  say  at  the  point  d,  is  represented  by  the  area  abcdd'c'b'a'  ; 
i.  e.,  the  area  included  between  the  curve  and  the  axis  of  X. 
Now  this  area  is 


Referring  to  Newton's  description  of  the  pressure  required  to 
account  for  gravitation,  we  see  that  the  expression  C  —  K/D 
exactly  fits  that  description.  (See  p.  I.) 

When  D  becomes  indefinitely  great  in  this  equation  we  have 
A  =  C.  Hence  C  is  the  ether  pressure  at  an  indefinitely  great 
distance  from  the  attracting  body.  K/D  is  plainly  the  pressure 
generated  beyond  the  distance  D.  That  is,  the  total  pressure  at 
distance  D  is  equal  to  the  pressure  at  infinite  distance  minus  the 
pressure  generated  beyond  distance  D.  This  is  equivalent  to 
stating  that  the  pressure  at  any  point  is  the  sum  of  all  the  pres- 
sures generated  between  that  point  and  the  body  producing  these 
pressures. 

Let  d  equal  the  diameter  of  an  electron  and  D  the  distance 
of  the  proximal  side  of  the  electron  from  the  attracting  body. 
Then  the  pressure  on  the  proximal  side  of  the  electron  is  C  —  K/D 
while  that  on  the  distal  side  is  C  -  K/(D  +  d).  The  difference 
between  these  pressures  is 


12         THEORY  OF  GRAVITATION    AND   RELATED   PHENOMENA. 

K_       K         K(D  +  d)  -  DK  =     _^_ 
D      D  +  d  D(D  +  d)         ~  D(D  +  d) ' 

But  d  vanishes  with  respect  to  D ;  hence  this  expression  becomes 
Kd/D2  for  ordinary  distances.  That  is,  gravitational  attraction, 
at  sensible  distances,  varies  inversely  as  the  square  of  the  distance 
from  the  attracting  body. 

From  what  has  been  said  of  gravitational  force  it  is  seen  that 
a  body  which  floats  in  space  near  another  body  is  acted  upon 
by  gravitational  force  in  much  the  same  way  as  a  bubble  is 
driven  upward  in  water.  It  is  in  a  medium  in  which  the  pressure 
increases  outward  from  the  attracting  body.  It  is  thus  driven 
inward  toward  the  body.  The  bubble  is  pressed  upon  below 
with  a  stronger  force  than  it  is  above,  and  is  hence  driven  upward. 

Mass. 

If  the  assumptions  as  to  the  meaning  of  motions  and  stresses 
in  the  ether  and  the  reasoning  above  are  correct,  it  is  seen  that 
the  gravitational  attraction  which  a  body  exerts  depends  not 
only  on  the  actual  mass  of  the  body  but  upon  the  Saturnian 
structure  of  the  atom  and  the  velocity  with  which  the  electrons 
move.  Hence,  if  I  am  correct,  we  must  distinguish  between 
mass  as  measured  by  the  attraction  of  other  bodies — that  is, 
by  inertia — and  mass  as  measured  by  attracting  power.  The 
former  depends  only  on  the  number  of  electrons  present,  and  is 
absolutely  invariable  for  a  given  quantity  of  matter.  On  the 
other  hand,  the  attracting  power  which  a  body  exerts  may  vary 
between  wide  limits,  if  the  velocity  of  its  electrons  changes.  If 
I  am  correct,  then,  Newton's  law  of  gravitation  needs  to  be 
restated.  According  to  Newton,  every  particle  of  matter  in 
the  universe  attracts  every  other  particle  with  a  force  varying 
as  the  product  of  the  masses  of  the  two  particles  and  inversely 
as  the  square  of  the  distance  between  them.  This  law  is  true 
only  of  the  attraction  which  one  body  exerts  on  another,  and 
then  only  when  the  mass  of  the  attracting  body  is  measured  by 
its  attracting  power,  while  the  mass  of  the  attracted  body  is 
measured  by  its  inertia.  I  would  state  this  law  thus:  every 
atomic  body  in  the  universe  attracts  every  other  body  (whether 


THEORY  OF  GRAVITATION  AND  RELATED  PHENOMENA.         13 

atomic  or  not)  with  a  force  which  varies  inversely  as  the  square 
of  the  distance,  and  directly  as  the  product  of  the  inertia  of  the 
attracted  body  by  the  amount  of  internal  energy  in  the  atoms  of 
the  attracting  body. 

Newton  believed,  and  stated  very  positively,  that  the  attrac- 
tion which  two  bodies  exert  on  each  other  does  not  consist  of 
two  separate  attractions,  but  that  it  is  one  and  the  same  attrac- 
tion. From  what  we  have  seen  above,  unless  there  is  some  flaw 
in  the  course  of  reasoning  followed,  the  attraction  which  two 
bodies  exert  on  each  other  must  be  considered  as  two  distinct 
and  independent  forces.  As  already  stated,  Newton  described  a 
pressure  which,  if  it  could  be  shown  to  exist  in  the  ether,  would 
account  for  gravitation.  Granting  my  fundamental  assumptions, 
I  have  shown  that  such  a  pressure  does  exist.  But  the  very 
pressure  described  by  Newton  does  not  call  for  gravitation  to  be 
mutual.  On  the  other  hand,  it  makes  two  separate  and  inde- 
pendent forces  of  the  attraction  between  two  bodies. 

If  my  reasoning  is  correct,  the  mass  of  the  earth  which  the 
sun  attracts  is  not  necessarily  equal  to  the  mass  of  the  earth 
which  attracts  the  sun.  The  attracted  mass  depends  only  on 
the  number  of  electrons  in  the  attracted  body.  The  attracting 
mass  depends  on  the  number  and  arrangement  of  these  electrons 
and  on  their  orbital  velocities. 

It  seems  clear  from  the  above  that  when  a  body  is  drawn 
toward  another  body  by  gravitational  attraction,  the  energy 
of  motion  which  the  attracted  body  gains  must  be  deducted 


H 


FIG.  10. 

from  the  orbital  energy  of  the  electrons  in  the  atoms  of  the  attrac- 
ting body.  The  attracting  body  is  not  itself  drawn  toward  the 
attracted  body  because  of  its  own  attraction;  it  merely  loses 
atomic  energy  as  the  attracted  body  approaches.  Let  us  con- 
sider what  would  happen  in  a  system  like  that  shown  in  Fig.  10, 
where  A  represents  the  attracting  body,  B  the  attracted  body 


14         THEORY  OF   GRAVITATION   AND   RELATED   PHENOMENA. 

(which  itself  exerts  no  attraction)  and  H  a  rigid  connection 
between  A  and  B.  Here  A  acts  on  the  ether  in  such  manner  as 
to  generate  pressure  at  all  points  in  the  ether,  the  total  amount 
of  this  pressure  at  any  point  being  C  —  K/D.  This  pressure 
is  greater  on  the  distal  than  on  the  proximal  side  of  B,  and 
hence  would  set  the  whole  system  in  motion.  But  all  the  energy 
of  motion  thus  acquired  would  be  deducted  from  the  internal 
energy  of  A ,  and  hence  would  weaken  by  so  much  the  attracting 
power  of  A.  The  system  would  tend  to  convert  all  this  energy 
in  A  into  energy  of  motion  of  the  whole  system,  after  which  it 
would  move  at  constant  velocity. 

The  idea  that  gravitational  attraction  is  mutual,  and  that  the 
force  which  draws  one  body,  A,  toward  another  body,  B,  is  one 
and  the  same  with  the  force  that  draws  B  toward  A,  involves 
a  theory  as  to  the  nature  of  the  stress  causing  gravitational  force, 
namely,  that  gravitational  force  is  due  to  distortion  of  the  ether, 
which,  in  consequence,  acts  like  a  bent  spring,  while  the  greater 
the  distortion,  the  less  the  force  it  exerts  The  ether  pressure 
which  Newton  described  so  accurately,  and  which  I  have  ac- 
counted for,  granting,  of  course,  my  fundamental  assumptions, 
does  not  call  for  mutual  attraction.  Newton  did  not  follow  out 
to  its  logical  conclusion  his  own  suggestion  of  an  ether  pressure, 
because  at  that  time  there  was  no  possible  way  of  accounting  for 
it.  Had  he  done  so,  he  would  certainly  have  discovered  that,  if 
gravitation  is  due  to  such  a  pressure,  it  is  not  mutual. 

Newton's  generalization  to  the  effect  that  gravitational  force 
is  proportional  to  the  product  of  the  masses  concerned  was  also 
an  unsupported  assumption.  On  this  point  J.  E.  Mills,  in  his 
excellent  treatment  of  this  subject  in  the  Journal  of  Physical 
Chemistry,  May,  1911,  remarks:  "When  Newton  proposed  his 
magnificent  generalization  he  had  no  proof  whatever  that  gravita- 
tional attraction  did  vary  as  the  product  of  the  masses  of  the 
attracting  bodies." 

Mills  further  calls  attention  to  the  fact  that  the  masses  of 
celestial  bodies  have  all  been  calculated  on  the  assumption  that 
Newton's  law  is  true.  I  have  shown  here  that  gravitational 
attraction  is  not  mutual  (granting,  of  course,  my  fundamental 
assumptions).  My  formula,  developed  directly  from  my  funda- 


THEORY   OF    GRAVITATION   AND   RELATED   PHENOMENA.         15 

mental  assumptions,  is  very  similar  to  that  given  by  Mills. 
My  statement  of  the  law  of  gravitation  (see  p.  12)  is  expressed 
by  the  formula 

%T^. 

in  which  F  represents  the  attraction  A  exerts  on  B,  M  is  the 
mass  of  B,  D  the  distance  between  them,  and  M'  is  a  factor 
depending  on  the  energy  represented  by  the  orbital  motion  of 
the  electrons  in  the  atoms  of  A .  Mills's  formula  for  the  attractive 
force  which  a  body  can  exert  is 

Force  = 


where  M  is  the  mass  of  the  attracting  body,  S  the  distance  to 
the  attracted  body,  and  ju  is  "an  intensity  factor."  (The  mass 
of  the  attracted  body  is  omitted  in  this  formula,  for  reasons 
given  by  Mills.) 

There  are  several  important  points  of  difference  between 
my  conclusions  and  the  ideas  advanced  by  Mills,  but  I  believe 
these  can  all  be  harmonized.  To  do  so  here,  however,  would 
require  too  much  space.  I  will  call  attention  to  only  one  of 
these  differences. 

Mills  states  (p.  455)  that  mass  is  "proportioned  to  the  attrac- 
tive forces  to  which  the  body  is  subjected."  This  is  true  in 
the  sense  that  the  amount  of  inertia  a  body  will  display  is  pro- 
portional to  these  forces.  I  find  two  kinds  of  mass.  One  of 
these  depends  on  the  volume  of  ether  displaced  by  the  electrons 
of  a  body.  This  kind  of  mass  is  measured  by  weight;  i.  e.,  by 
the  attractions  which  other  bodies  exert  on  the  body.  It  is  the 
omitted  mass  of  the  attracted  body  in  Mills's  formula.  The 
other  kind  is  a  function  of  the  internal  energy  of  the  atoms  of 
the  body.  It  depends  not  only  on  the  volume  of  ether  displaced 
(the  M  of  Mills's  formula),  but  on  the  energy  of  motion  of  the 
electrons  in  the  atoms  (the  /*  factor  in  Mills's  formula). 

According  to  my  theory,  when  a  body  is  raised  from  the 
earth,  the  apparent  potential  energy  which  it  gains  is  not  stored 
in  the  ether  as  some  impossible  kind  of  stress,  as  is  generally 


1 6         THEORY  OF   GRAVITATION  AND   RELATED  PHENOMENA. 

assumed  to  be  the  case.  (In  this  connection  Mills  quotes 
Farady  as  repeatedly  asserting  his  belief  that  no  force  with  the 
properties  usually  ascribed  to  gravitation  could  exist.  On  my 
theory  no  such  paradoxical  assumptions  are  necessary.)  The 
energy  which  appears  to  be  potential  energy  of  the  raised  body  is, 
on  my  theory,  simply  added  to  the  energy  represented  by  the 
orbital  motion  of  the  electrons  in  the  earth's  atoms.  When  the 
body  falls  again,  this  energy  is  transferred  from  the  earth's  atoms 
to  the  falling  body  by  means  of  the  ether.  When  the  body  strikes 
the  earth  this  energy  is  converted  into  heat. 

There  is  another  striking  parallel  between  my  conclusions  and 
those  of  Mills.  He  concludes  that  the  amount  of  gravitational 
force  which  a  body  can  exert  is  limited  and  definite.  My  con- 
clusion is  that  the  amount  of  energy  of  motion  which  a  given  body 
can  generate  by  attraction  on  other  bodies  is  similarly  limited 
and  definite.  All  the  energy  of  motion  thus  generated,  according 
to  my  view,  is  deducted  from  the  internal  energy  of  the  atoms  of 
the  attracting  body.  When  this  supply  is  exhausted,  the  body 
no  longer  exerts  attraction.  It  is  suggested  elsewhere  in  this 
paper  that  this  may  be  the  condition  of  comets,  and  that  this 
fact  -may  account  for  their  disintegration,  as  well  as  for  their 
apparent  lack  of  attracting  power. 

The  phenomena  of  falling  bodies  prove  the  attraction  is  pro- 
portional to  the  mass  of  the  attracted  body;  and  this  is  what  my 
theory  calls  for.  But  these  phenomena  do  not  prove  that  the 
force  is  proportional  to  the  mass  of  the  attracting  body.  On 
my  theory,  the  attraction  is  proportional  to  the  mass  of  the 
attracting  body  only  so  long  as  the  internal  energy  of  the  atoms 
of  the  attracting  body  remains  the  same.  There  are  no  known 
facts  not  in  accord  with  this  conclusion. 

Direction  of  Attraction. 

On  the  theory  here  presented,  the  direction  in  which  gravita- 
tional force  tends  to  move  an  attracted  body  would  be  wholly 
independent  of  any  motion  which  the  attracted  body  might 
have.  I^the  attracting  body  were  stationary  in  the  ether,  that 
is,  if  its  attracting  center  were  stationary,  all  bodies  would  be 
attracted  exactly  toward  this  center,  no  matter  what  motions 


THEORY  OF  GRAVITATION  AND   RELATED   PHENOMENA.         I/ 

the  attracted  bodies  might  have.  But  if  the  attracting  body 
itself  is  in  motion,  then  the  attracting  center  will  be  somewhere 
on  the  locus  of  the  real  center  of  the  attracting  body,  behind  the 
real  center.  In  this  connection  Drude  remarks:*  "One  can 
indeed  deduce  the  general  result,  that  by  acceptance  of  the 
latter  (i.  e.,  the  effect  of  the  sun's  motion  through  space,  if  gravi- 
tational force  is  propagated  at  a  finite  velocity)  anomalies  in 
the  motion  of  the  perihelion  of  the  planets  may  be  explained." 
Newton  stated  that  a  perihelion  motion  arises  if  one  introduces, 
instead  of  the  square,  a  somewhat  different  power  of  the  distance, 
and  Hall  has  shown  that  an  exponent  2.00000016,  instead  of  2, 
will  account  for  the  perihelion  movement  of  Mercury.f  From 
what  has  been  said  above  it  seems  probable  that  attraction  is 
not  directed  exactly  toward  the  center  of  the  attracting  body 
when  the  latter  is  in  motion,  but  rather  to  a  point  occupied  by 
this  center  shortly  before. 

It  is  also  possible  that  there  is  a  sensible  variation  from  the 
law  of  inverse  squares.  In  the  first  place,  the  formula  for 
gravitational  pressure  is  arrived  at  by  omitting  certain  infinitesi- 
mal terms,  which  make  the  exponent  of  D  a  little  greater  than  2. 
This  excess,  however,  is  exceeding  small,  and  may  not  produce 
measurable  effects  in  long  periods  of  time.  We  could  calculate 
it  if  we  knew  the  diameter  of  the  electron. 

Pressure  in  the  Ether. 

Depending  on  the  correctness  of  the  fundamental  assumptions 
on  which  the  present  theory  is  based,  it  has  been  shown  that 
there  is  a  mechanism  by  which  the  atom  maintains  an  "even- 
powered"  pressure  in  the  ether  about  it.  The  magnitude  of 
this  pressure  might  possibly  be  calculated;  but  to  do  this  it 
would  be  necessary  to  know  the  diameter  and  velocity  of  the 
electrons,  the  size  of  their  orbits,  and  the  rate  at  which  pressures 
are  propagated  through  the  ether.  I  have  calculated  the  pres- 
sure which  the  electrons  of  an  atom  of  iron  could  maintain  if 
they  moved  as  do  the  molecules  of  a  gas,  with  a  velocity  of  12,000 
miles  per  second,  in  a  space  equal  to  the  volume  of  the  iron 

*  Ann.  d.  Phys.  &  Chem.,  Vol.  62. 
t  Smithsonian  Rep.,  1876,  p.  205. 


1  8         THEORY  OF   GRAVITATION  AND   RELATED   PHENOMENA. 

atom.  The  value  of  this  pressure  is  io19  dynes  per  square  centi- 
meter. The  pressure  caused  by  a  single  atom  under  my  theory 
of  gravitation  cannot  exceed  this,  for  this  pressure  was  calculated 
on  the  assumption  that  the  total  kinetic  energy  of  the  electrons 
is  utilized  in  maintaining  this  pressure.  How  much  smaller 
the  actual  pressure  is  is  uncertain  ;  but  it  would  probably  be  much 
smaller.  Yet  it  is  seen  that  a  single  atom  may  possibly  generate 
in  the  ether  about  it  an  enormous  pressure.  When  it  is  re- 
membered that  every  atom  in  the  universe  generates  such 
pressure,  the  sum  of  all  these  pressures  is  beyond  comprehension. 
The  theory  certainly  provides  pressure  sufficient  to  account  for 
the  phenomena  of  gravitation. 

Chemical  Affinity. 

It  has  been  shown  (p.  9)  that  the   formula    for  the  strength 

of  the  magnetic  field  about  an  atom  is  (2KDd  +  Kd2)/[Dz(D+d)2]. 

The  gravitational  force  generated  at  the  same  distance  is 


Equating  these  two  values  we  have 
2KDd  -  Kd*  K 


That  is,  at  the  point  at  which  D  =  (^2  +  i)d,  the  magnetic 
field  is  equal  to  the  gravitational  force  generated.  There  is 
thus  a  point  at  which  two  atoms,  properly  oriented  with  reference 
to  each  other,  would  be  in  a  position  of  equilibrium,  being  re- 
pelled from  each  other  by  magnetic  force,  and  pulled  toward 
each  other  by  gravitational  force.  We  may  have  here  a  hint  as 
to  the  nature  of  chemical  affinity. 

Relation  of  Molecular  Attraction  (cohesion)  to  Distance. 

It  is  known  that  to  increase  the  distance  between  the  molecules 
of  a  homogeneous  liquid  by  a  given  fraction  of  itself,  the  amount 
of  heat  energy  necessary  is  proportional  to  the  mass  of  the 
liquid. 

Let  A  represent  the  attraction  between  two  molecules  at  unit 
distance  from  each  other.  Assume  the  law  of  relation  between 
this  attraction  and  distance  to  be  such  that  the  attraction 


THEORY  OF  GRAVITATION  AND   RELATED  PHENOMENA.         19 

between  two  molecules  at  distance  5  varies  as  some  power  of  S 
(whether  directly  or  inversely  to  be  determined  later).  The 
attraction  at  distance  S  then  becomes  ^45*,  where  X  is  to  be 
determined.  In  overcoming  this  attraction  by  moving  one  of 
the  molecules  through  a  distance  nS,  the  energy  expended  is 

s  A  Cz+1 

ASxdS  =^r-(nx+l  -  i), 


X  -f-  I 


which  may,  for  convenience,  be  written  KSX+1,  since  n  and  x  are 
constants. 

Now,  the  number  of  molecules  at  distance  5  from  a  given 
molecule  is  proportional  to  S2.  Hence,  the  energy  required 
to  move  an  elemental  spherical  layer  of  molecules,  at  distance 
S  from  a  given  molecule,  is 

KS*+1  X  KiS*  =  K2SX+3. 

The  total  energy  required  to  overcome  the  attraction  of  a  single 
molecule  at  the  center  of  the  body  for  all  the  elemental  layers 
concentric  about  it  is  evidently 


1 


K2Sx+3dS, 
'o 

where  R  represents  the  radius  of  the  body,  which,  for  convenience, 
is  assumed  to  be  spherical.  This  integration  gives  KzRx+*/x  +  4, 
which  may  be  written  K3RX+4.  Now  every  molecule  in  the 
mass,  except  a  negligible  number  near  its  surface,  exerts  attrac- 
tions which  require  like  amounts  of  energy  to  overcome.  The 
total  number  of  molecules  about  which  such  a  field  of  force 
exists  is  proportional  to  the  volume  of  the  sphere  and  may, 
therefore,  be  represented  by  K±R3,  where  K±  is  a  constant,  and 
R  the  radius  of  the  sphere.  The  total  energy  required  to  expand 
the  body  is,  therefore,  KBRX+4  X  K*R3  =  K5RX+7.  But  we 
know  that  this  is  proportional  to  the  mass,  and  hence  to  the 
volume  of  the  sphere.  Hence  K5RX+7  =  K&R3.  Since  R  may 
have  any  value,  let  R  =  i.  Then  K5  =  K&,  and  Rx+7  =  R3. 
.'.#-{-7  =  3.  •'.#=  —  4.  Hence,  the  force  of  attraction 
between  neighboring  molecules  appears  to  vary  inversely  as 
the  fourth  power  of  the  distance. 


2O         THEORY   OF  GRAVITATION  AND   RELATED   PHENOMENA. 

Can  this  force  be  identified  with  any  of  the  forces  found  in 
the  development  of  the  foregoing  theory?  I  believe  that  it  is 
not  inconsistant  with  these  forces.  According  to  the  theory, 
the  atom  is  a  magnet.  It  has  been  suggested  that  the  phenomena 
of  chemical  affinity  are  due  to  this  property  of  atoms.  Now  if 
two  atoms  be  properly  placed  with  reference  to  each  other, 
each  tends  to  cancel  the  magnetic  field  of  the  other.  Yet  two 
atoms  can  not  entirely  cancel  each  other's  fields.  There  is 
thus  a  magnetic  field  about  a  molecule  which  may  be  looked 
upon  as  a  "left  over"  from  chemical  affinity.  In  Fig.  n, 

—  • 

P  , 

b 

FIG.  ii. 

let  a  and  b  represent  two  atoms  so  placed  as  to  be  in  equilibrium  ; 
in  this  position  they  tend  to  cancel  each  other's  magnetic  field. 
Let  P  represent  a  point  in  the  ether  in  the  vicinity  of  the  mole- 
cule ab.  Let  D  represent  the  distance  of  P  from  &,  and  D  +  d 
its  distance  from  a.  Now,  6's  magnetic  field  at  P  may  be  repre- 
sented as  K/D3,  since  it  varies  inversely  as  the  cube  of  the  dist- 
ance. Similarly,  the  strength  of  a's  field  at  P  is  K/[(D  +  d)3\. 
The  resultant  strength  of  field  at  P  is,  therefore, 

#  K 


D3      (D  -f  d)3  D3(D  +  d)3 

If  d  is  small  in  comparison  with  D,  this  becomes 


D*        D*' 

Hence  the  magnetic  field  about  a  chemically  saturated  molecule 
varies  inversely  as  the  fourth  power  of  the  distance.  Thus  we 
find  a  force  varying  with  distance  as  does  the  molecular  force 
considered  above. 

There  is  the  further  fact  to  be  considered  that  a  magnetic 
field  is  modified  by  the  presence  of  other  magnetic  bodies. 
Hence  it  is  possible  that  the  magnetic  field  of  a  molecule  sur- 


THEORY   OF   GRAVITATION  AND   RELATED   PHENOMENA.         21 

rounded  by  other  molecules  may  extend  only  a  short  distance,  a 
fact  which  may  have  something  to  do  with  the  rapid  decrease  of 
molecular  force  as  the  distance  increases. 

POSSIBLE   RELATION   BETWEEN   TEMPERATURE  AND  GRAVITA- 
TIONAL ATTRACTION. 

It  has,  of  course,  long  been  known  that  weight  is  independent 
of  the  temperature  of  the  weighed  body.  But  if  the  theory  of 
gravitation  here  presented  is  true,  there  is  a  possibility  that  the 
temperature  of  a  body  may  be  a  factor  in  the  gravitational  force 
it  exerts.  This  would  be  the  case  if  there  is  any  exchange  of 
energy  between  the  internal  energy  of  the  atom,  represented  by 
the  revolution  of  the  electrons  in  a  Saturnian  system,  and  the 
heat  energy  of  the  atom,  represented  by  its  motion  as  a  whole. 
This  relation,  however,  cannot  be  a  direct  one,  as  the  following 
considerations  will  show: 

It  is  estimated  that  the  electrons  in  an  atom  under  ordinary 
conditions  move  with  a  velocity  of  about  14,000  miles  per  second. 
The  amount  of  internal  energy  in  the  atoms  of  a  pound,  say  of 
copper,  would  thus  be  (i/2MV*  poundals,  or)  n  X  io13  ft.  Ibs. 
Assuming  that  the  specific  heat  of  copper  between  o°  C.  absolute 
and  300°  C.  absolute  is  .091  (it  is  probably  less  than  this),  the 
total  heat  energy  in  a  pound  of  copper  at  ordinary  temperatures 
is  about  38,000  ft.  Ibs.  The  former  number  is  a  little  less  than 
3  thousand  million  times  the  latter.  Hence,  if  we  double  the 
absolute  temperature  of  the  copper,  and  if  all  the  energy  thus 
added  were  converted  into  internal  atomic  energy,  the  increase 
in  this  internal  energy  would  be  infinitesimal,  and  not  capable 
of  measurement. 

But  if  we  imagine  the  internal  energy  of  the  atom  to  be  reduced 
by  some  means  to  a  very  low  point,  then  an  increase  in  tempera- 
ture might  produce  a  perceptible  effect  on  the  gravitational  force 
exerted.  Such  an  assumption  would  explain  a  very  puzzling 
phenomenon  exhibited  by  comets.  We  may  assume  these  bodies 
to  be  extremely  cold ;  also  that  this  condition  has  existed  in  them 
for  ages.  Under  such  conditions  there  is  a  possibility  that  atomic 
collisions  may  have  transformed  a  considerable  portion  of  the 
internal  energy  of  the  atoms  into  heat,  and  that  this  heat  has 


22         THEORY  OF   GRAVITATION  AND   RELATED   PHENOMENA. 

become  dissipated  by  radiation  into  space.  The  matter  com- 
posing a  comet  would  in  this  way  lose  much  of  its  gravitational 
force.  These  bodies  are  known  to  consist  of  flocks  of  meteorites ; 
possibly  they  are  disintegrated  planets  or  satellites  of  our  own 
or  of  formerly  existing  stellar  systems.  As  they  approach  the 
sun  they  first  expand  and  then  contract  in  size.  Thus,  Enke's 
comet  is  300,000  miles  in  diameter  when  at  a  distance  of  130 
million  miles  from  the  sun,  but  contracts  to  a  diameter  of  only 
10,000  to  14,000  miles  at  its  perihelion  distance  of  33  million 
miles.  If  we  may  assume  the  temperature  of  this  body  to  be 
very  near  the  absolute  zero  at  its  aphelion,  then  the  increase  in 
temperature  on  approaching  the  sun  must  be  relatively  large. 
Now,  if  a  considerable  portion  of  this  heat  energy  is  converted 
into  internal  energy  of  the  atoms,  then  the  increase  in  gravi- 
tational force  resulting  might  account  for  the  diminution  in 
size  of  the  comet. 

It  may  also  be  suggested  here,  though  it  has  no  relation  to  the 
theory  under  discussion,  that  the  increased  frequency  of  collision 
between  the  particles  of  a  comet  as  the  comet  contracts  may  give 
rise  to  the  cometary  tail  by  thus  freeing  small  particles  of  dust 
and  the  like  adhering  to  the  meteorites  composing  the  body  of 
the  comet. 

If,  when  a  body  becomes  cold,  and  remains  so  for  countless 
ages,  the  internal  energy  of  its  atoms  may,  by  being  slowly  con- 
verted into  heat,  become  dissipated,  our  theory  offers  an  inter- 
esting explanation  of  a  self-perpetuating  universe  at  all  times 
similar  to  that  which  we  know.  As  the  central  body  of  a  system 
loses  its  power  of  gravitational  attraction  its  satellites  gradually 
increase  their  orbits  and  lose  in  velocity,  finally  giving  a  widely 
scattered  group  of  bodies  of  slight  motion  relative  to  their 
former  center  of  attraction.  Finally,  because  of  rotation  on 
their  axes,  all  these  bodies,  including  the  central  one,  become 
disintegrated  into  meteorites,  which  ultimately  scatter  through- 
out the  universe.  The  smaller  bodies,  with  presumably  smaller 
rotational  velocities,  disintegrate  more  slowly  than  the  larger, 
and  thus  persist  longer.  They  thus  have  more  chance  of  being 
drawn  into  other  systems  as  comets,  before  they  become  com- 
pletely scattered  as  single  fragments.  Occasionally  the  larger 


THEORY  OF  GRAVITATION  AND   RELATED  PHENOMENA.        23 

bodies,  before  complete  disintegration,  meet  similar  meteoric 
groups,  the  heat  generated  by  collision  setting  up  attraction 
anew,  thus  giving  rise  to  new  attracting  centers  which  develop 
planetary  systems  about  them  from  the  fragments  of  two  former 
systems. 

We  have  been  repeatedly  told  that  space  is  filled  with  "dark" 
stars — dead  suns  that  have  lost  their  heat.  Perhaps,  after  all, 
this  is  not  the  case.  Such  bodies  may  be  only  temporary;  they 
may  soon  disintegrate  and  scatter  out  through  space  as  meteor- 
ites. The  heat  energy  thus  dissipated  into  space  may  be  in 
large  part  absorbed  by  other  bodies,  in  the  manner  in  which  an 
incandescent  gas  absorbs  rays  of  the  same  length  it  emits.  If 
such  is  the  case,  then  there  is  not  necessarily  any  permanent 
loss  of  energy  by  dissipation  into  space,  and  the  universe  thus 
becomes  self-perpetuating. 

Periodicity  of  Sun  Spots. 

It  has  been  known  since  1851  that  the  time  between  maximum 
sun  spot  periods  is  roughly  equal  to  the  period  of  revolution 
of  the  planet  Jupiter.  If  the  present  theory  of  gravitation  is 
correct,  it  suggests  an  explanation  of  this  phenomenon.  When 
Jupiter  is  in  perihelion  it  is  approximately  46,000,000  miles 
nearer  the  sun  than  when  in  aphelion,  and  has  a  correspondingly 
greater  velocity.  The  increased  energy  represented  by  this 
increased  motion  is  assumed  to  be  derived  from  the  internal 
energy  of  the  sun's  atoms.  If  this  is  true,  the  velocity  of  the 
electons  in  the  sun's  atoms  must  be  smaller  when  Jupiter  is  in 
perihelion  than  when  she  is  in  aphelion.  Hence,  when  the 
planet  is  in  aphelion,  there  is  a  possibility  that  the  greater 
velocity  of  the  electrons  in  the  atoms  of  the  sun  causes  a  greater 
degree  of  atomic  degradation  of  the  nature  of  that  seen  in 
radium,  and  related  radio-active  substances.  It  is  reasonable 
to  suppose  that  this  would  affect  the  sun's  electrical  activity. 
Thus,  the  approach  of  a  planet  toward  the  sun  would  tend  to 
decrease  this  activity,  while  it  would  increase  as  the  planet 
recedes. 

Assuming  that  the  approach  or  recession  of  a  planet  does  cause 
corresponding  changes  in  the  electrical  activity  of  the  sun  by 


24         THEORY  OF   GRAVITATION   AND   RELATED   PHENOMENA. 

decreasing  or  increasing  atomic  degradation,  Mr.  J.  W.  Froley 
and  the  writer  have  calculated  the  relative  effects  of  all  the 
planets  on  the  sun's  electrical  activity.  The  effects,  if  any, 
produced  by  Jupiter  and  Saturn  are  so  large  when  compared 
with  those  of  all  the  other  planets  combined  that  the  latter  may 
be  neglected.  Fig.  12  shows  the  relation  between  sun  spot 
frequency  and  the  combined  effect  of  Jupiter  and  Saturn,  on 
the  assumptions  here  made.  The  nearly  regular  curve  repre- 
sents the  combined  effect  of  the  two  large  planets,  while  the  less 
regular  curve  shows  sun  spot  frequency.  There  is  at  least  a 
remarkable  coincidence  in  these  curves.  It  will  be  noticed  that 


FIG.  12.  Relation  of  sun  spots  to  combined  action  of  Jupiter  and  Saturn 
on  the  sun.  The  smooth  curve  represents  the  combined  effect  of  the  two 
planets;  the  less  regular  curve,  the  frequency  of  sun  spots. 

in  5  of  the  10  sun  spot  minima  shown  in  Fig.  12,  the  sun  spot 
minimum  occurs  just  before  the  close  of  the  period  of  rapid 
decrease  of  activity.  These  are  the  sun  spot  minima  occurring 
about  the  years  1784,  1843,  1855,  1867,  and  1878.  Each  of 
these  5  minima  is  succeeded  by  a  maximum  which  occurs  at  the 
time  of  most  rapid  increase  in  activity.  In  the  other  5  cases, 
namely,  in  1775,  1797,  1810,  1822,  and  1833,  the  sun  spot  mini- 
mum occurs  just  after  the  minimum  activity  is  reached,  and, 
with  only  one  exception,  the  succeeding  sun  spot  maximum 
occurs  very  nearly  at  the  time  of  maximum  activity. 

If  it  is  true  that  the  eccentricity  of  the  orbit  of  these  two 
great  planets  is  the  cause  of  sun  spot  periods,  is  it  not  possible 
that  the  variability  of  some  stars  may  be  similarly  accounted 
for?  Should  a  star  have  several  relatively  large  attendants, 
each  with  a  highly  eccentric  orbit,  the  resulting  variations  of 
electrical  activity  might  not  only  be  considerable,  but  the  curve 


THEORY  OF   GRAVITATION  ANtf '  RELAT'EI*   PHENOMENA.  "     25 

of  variability  would  be  very  complex.  A  proper  analysis  of 
such  a  curve  could  be  made  to  reveal  not  only  the  number  of 
the  attendants  concerned,  but  their  time  of  revolution  about 
the  star. 

There  is  reason  to  believe  that  there  is  actually  a  relation 
similar  to  that  here  predicated  between  sun  spots  and  electric 
activity  on  the  sun. 

The  writer  desires  to  express  his  obligation  to  Mr.  J.  W.  Froley, 
whose  constant  advice  on  mathematical  phases  of  the  theory  has 
been  exceedingly  helpful;  also  to  Dr.  W.  J.  Humphries,  who  has 
read  the  manuscript,  and  offered  helpful  suggestions  in  the 
treatment  of  some  of  the  problems  connected  with  the  working 
out  of  the  theory. 

CONCLUSION. 

A  theory  which  offers  a  rational  explanation  of  hitherto  un- 
explained phenomena  is  useful  for  two  purposes.  In  the  first 
place  it  enables  the  student  to  see  how  a  thing  may  be  caused, 
and  thus  renders  intelligible  what  before  was  only  a  jumble  of 
apparently  unrelated  facts.  It  helps  the  mind  in  forming  a 
conception  of  facts.  It  is,  of  course,  unnecessary  to  caution  the 
wise  teacher  that  any  unproved  theory  should  be  presented  as  a 
theory,  not  as  a  fact.  In  the  second  place,  a  good  theory  usually 
illuminates  new  fields,  and  points  to  hitherto  unknown  facts. 
Such  a  theory  suggests  new  investigations,  and  herein  lies  the 
principal  value  of  a  working  theory.  Unfortunately,  the  present 
theory,  while  it  points  to  many  new  facts,  reveals  nothing  which 
is  certainly  within  the  reach  of  experiment.  There  is,  however, 
one  possible  direction  in  which  experiments  might  reveal  some- 
thing of  interest.  Different  elementary  substances,  such  for 
instance,  as  lead  and  copper,  which  differ  greatly  in  atomic 
weight,  might  possibly  differ  also  in  the  gravitational  attraction 
which  a  given  mass  of  the  two  substances  exerts.  This  depends 
on  whether  the  internal  energy  of  the  atom  is  proportional  to 
its  mass  alone,  and  on  whether  attracting  power  varies  directly 
as  this  internal  energy,  or  as  some  other  function  of  the  velocity 
of  the  electrons  in  the  atom. 


26         TfrEOlT?  Olf  GRAViYATidtf  AND   RELATED   PHENOMENA. 

It  may  be,  also,  that  a  freshly  fallen  meteorite  might  differ  in 
its  attracting  power  from  a  terrestrial  body  of  the  same  weight. 

It  is  hardly  necessary  to  point  out  that  the  kind  of  ether 
presupposed  in  the  present  theory  is  consistent  with  the  phe- 
nomena of  light  and  other  forms  of  radiant  energy. 

It  may  also  not  be  out  of  place  here  to  suggest  that  the  "ether 
drift,"  if  it  occurs  as  here  supposed,  might  possibly  be  detected 
by  measuring  the  wave  length  of  light  transmitted  in  different 
directions  at  the  same  time  and  place. 


